Fisher's Equation (I solved it, now need to know how to analyze my plot)

  • Thread starter takbq2
  • Start date
  • Tags
    Plot
In summary, the conversation discusses solving Fisher's equation, which is a PDE involving the speed of a wave front of solutions and its dependence on the amplitude and length of the initial population with a "mutant gene". The speaker has managed to solve the equation and create plots, but is unsure how to analyze them to find the desired relationships. They also ask if anyone has experience with the Fisher equation.
  • #1
takbq2
32
0

Homework Statement



I am asked to solve Fisher's equation, i.e. the PDE ut = uxx+u(1-u) .

Then I am asked to describe how the speed of the wave front of solutions to it depend on the amplitude of the initial population with the "mutant gene"

and likewise how does it (the wave front of solutions) depend on the length of the spatial interval occupied by the initial population with the "mutant gene".

I managed to solve the equation and come up with some nice looking plots, but I'm not sure how to analyze them to find the relationships.


Homework Equations





The Attempt at a Solution



I solved the equation, just don't really understand the solutions. Need to find the relationships stated above. I attached a JPEG of my plot.
 

Attachments

  • fishplot.jpg
    fishplot.jpg
    45.8 KB · Views: 360
Physics news on Phys.org
  • #2
anyone dealt with the fisher equation?
 

FAQ: Fisher's Equation (I solved it, now need to know how to analyze my plot)

What does Fisher's equation represent?

Fisher's equation is a mathematical model used in population genetics to predict the rate of change of a gene in a population over time.

How is Fisher's equation solved?

Fisher's equation can be solved using various numerical methods, such as Euler's method or Runge-Kutta method, or by using analytical methods such as separation of variables or Laplace transforms.

What does the plot of Fisher's equation represent?

The plot of Fisher's equation represents the change in gene frequency over time in a population. It can also show the stability or instability of a population's gene pool.

How do I analyze my plot of Fisher's equation?

To analyze your plot of Fisher's equation, you can look for patterns or trends in the change of gene frequency over time. You can also compare your plot to known solutions or use mathematical techniques, such as stability analysis, to interpret the behavior of the population.

What are some real-world applications of Fisher's equation?

Fisher's equation has been used to study the evolution of diseases, such as HIV and influenza, and to predict the spread of antibiotic resistance in bacteria. It has also been applied in fields such as ecology, economics, and epidemiology to model population dynamics and predict future trends.

Similar threads

Explaining a physical model (differential equation)
Replies
27
Views
2K
How to Solve Plotting Issues in Mathematica 7?
Replies
1
Views
1K
Solve Laplace equation on rectangle domain
Replies
5
Views
2K
MATLAB Plot a non homogeneous DPE -- Sum two plots in Matlab?
Replies
1
Views
1K
Analyzing PDE BVP for ut + ux = 0 with given boundary condition
Replies
1
Views
1K
Solving a 2D PDE using the Fourier Transform
Replies
3
Views
2K
Solving D'alembert Equation for Wave eq. u(4,1) & u(1,4)
Replies
1
Views
2K
Solving PDE & Plotting -20 < x < 20, t = 0,1,2,...10
Replies
10
Views
3K
How can I solve this 2nd degree differential equation?
Replies
2
Views
1K
I Gap Equations Plotting Error in Python: Need Help Debugging
Replies
7
Views
981

Hot Threads

Recent Insights

Back
Top